Explorer Math

Thursday, February 16, 2017

Saving the Baiji

With less than twenty left in the world, the Baiji dolphin is one of the most endangered species on Earth. But you have a solution. You've invented a duplicating machine so you can put one dolphin in and get two out! But right now you only have a prototype that can duplicate coins. But once you have enough money from the prototype, you can build the full size duplicator. Test it out below after you solve the trapezoid problem.

Good luck!

Length of the midsegment:

Solve this problem to test the duplicator machine!

Wednesday, January 4, 2017

Rotations and Reflections

Congratulations, you solved the ancient Greek paradox of Zeno. Euclid was so happy with your explanation that he decided to help you!

He looked through the code and found a mistake in your tables of rotations and reflections. Your time machine does a series of translations, rotations and reflections through four-dimensional space. Unfortunately, your programmer put in the wrong coordinate transformations in your master table.

Euclid is too excited about building his own computer to help you complete the task so you're on your own. Simply select the name of the transformation that corresponds to each of the possible coordinate changes below. There are four rotations (90, 180, 270 & 360°) and four reflections (across four different lines: the x-axis, the y-axis, the line y = x, and the line y = –x).

Good luck!

(If you're thinking about just guessing, there are 8*7*6*5*4*3*2*1 = 40,320 possible answers!!!)

Keep x & y	New x: keep sign	New x: change sign
New y: keep sign	`(x,y) → (x,y)`	`(x,y) → (-x,y)`
New y: change sign	`(x,y) → (x,-y)`	`(x,y) → (-x,-y)`

Switch x & y	New x: keep sign	New x: change sign
New y: keep sign	`(x,y) → (y,x)`	`(x,y) → (-y,x)`
New y: change sign	`(x,y) → (y,-x)`	`(x,y) → (-y,-x)`

Complete the tables to fix your time machine!